Kummer's Theorem

The identity

or equivalently

where  is a hypergeometric function and  is the gamma function. This formula was first stated by Kummer (1836, p. 53).

REFERENCES:

Bailey, W. N. "Kummer's Theorem." §2.3 in Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 9-10, 1935.

Kummer, E. E. "Ueber die hypergeometrische Reihe." J. für Math. 15, 39-83, 1836.